Ground state energy of Bose particle system

Elliolt H. Lieb, Jakob Yngvason

Hock-Kee Sim, R. Tao, Fa Yueh Wu

The ground state of a two-dimensional charged quantum system is studied using the method of correlated-basis functions. For particles obeying the Bose-Einstein statistics we compute the ground-state energy variationally for all particle densities using the Bijl-Dingle-Jastrow trial wave function. The Bose ground-state energy and wave function so determined are used next to study the Fermi system. We compute the Fermi ground-state energy using a cluster expansion approach, which is again valid for all particle densities, and find that the ground state is paramagnetic. While these calculations provide variational upper bounds to the ground-state energies, we also establish independent lower bounds to the ground-state energies.

Sang‐Hoon Kim, CHUL KU KIM, Mukunda P. Das

The ground-state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order na3 in the particle depletion and ground-state energy density of a dilute Bose gas system, which corresponds to the density fluctuation resulting from the excited states. Considering a two-body interaction only, the coefficient of the na3 term is shown to be 2(π-8/3) for the particle depletion, and 16(π-8/3) for the ground-state energy density.

Élliott H. Lieb, Jakob Yngvason

Jon Links, Shao-you Zhao A

We employ an exact Bethe ansatz solution to study the repulsive Bose–Hubbard dimer model. Using a continuum approximation we solve for the ground state root density and in turn compute the ground state energy per particle. The formula so obtained is accurate for a finite-sized system in the weak coupling limit. Surprisingly, the formula diverges from the numerically calculated value as the number of particles increases. This indicates that the formula fails to predict the ground state energy per particle in the thermodynamic limit.

Élliott H. Lieb, Jan Philip Solovej